{"id":4317,"date":"2012-10-15T22:05:18","date_gmt":"2012-10-15T22:05:18","guid":{"rendered":"http:\/\/SchoolTutoring.com\/help\/?p=4317"},"modified":"2014-12-02T08:31:59","modified_gmt":"2014-12-02T08:31:59","slug":"algebra-symbolic-logic","status":"publish","type":"post","link":"https:\/\/schooltutoring.com\/help\/algebra-symbolic-logic\/","title":{"rendered":"Algebra: Symbolic Logic"},"content":{"rendered":"

Proposition:<\/h4>\n

A proposition is a statement which is either true or false but not both. For example, 9<10 (true) is proposition; 4+9=14 is a proposition (false). The truthfulness or falsity of the proposition is called truth value<\/em><\/strong> of the proposition. If a proposition is true, then its truth value is denoted by T<\/em><\/strong> and if it is false then its truth value is denoted by F<\/em><\/strong>.<\/p>\n

Logical connectives and compound propositions:<\/h4>\n

Usually we combine any two propositions by means of the phrases and, or, if then, if and only if.<\/em><\/strong> These are called the logical connectives<\/strong> and the propositions which are involved with the logical connectives are called the compound propositions<\/strong>. A proposition with out any connectives is called a simple proposition.<\/p>\n

Example:<\/strong><\/p>\n

a)\u00a0\u00a0\u00a0\u00a0\u00a0 If you work hard then you pass the exam.<\/p>\n

b)\u00a0\u00a0\u00a0\u00a0\u00a0 I like Math and my brother likes Science.<\/p>\n

Conjunction:<\/h5>\n

It is a compound proposition whose components are connected by the word and<\/em><\/strong>. If p and q are any two simple propositions then the p and q<\/strong> is denoted by p^q<\/strong>. p^q is true only when both p and q are true. Otherwise it is false.<\/p>\n

\"\"<\/a><\/p>\n

Disjunction:<\/strong><\/h5>\n

It is a compound proposition whose components are connected by the word or<\/em><\/strong>. If p and q are any two simple propositions then the p or q <\/strong>is denoted by pvq<\/strong>. pvq is true only when either p or q are true. i.e. pvq is false only when both p and q are false.<\/p>\n

\"\"<\/a><\/p>\n

Conditional statement:<\/h5>\n

It is a compound proposition whose components are connected by the phrase if then<\/em><\/strong>. If p and q are any two simple propositions then the if p then q<\/strong> is denoted by p<\/strong>\u00e0q<\/strong>. p\u00e0q is true only when p is true and q is false. Otherwise it is false.<\/p>\n

\"\"<\/a><\/p>\n

Biconditional statement:<\/h5>\n

It is a compound proposition whose components are connected by the phrase if and only if <\/em><\/strong>. If p and q are any two simple propositions then the if p if and only if q<\/strong> is denoted by p\u2194q<\/strong>. p\u2194<\/strong>q is true only when p and q have the same truth values. Otherwise it is false.<\/p>\n

\"\"<\/a>
\n<\/strong>
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SchoolTutoring Academy is the premier educational services company for K-12 and college students. We offer tutoring programs for students in K-12, AP classes, and college. To learn more about how we help parents and students in Alaska visit: Tutoring in Alaska.<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"

Proposition: A proposition is a statement which is either true or false but not both. For example, 9<10 (true) is proposition; 4+9=14 is a proposition (false). The truthfulness or falsity of the proposition is called truth value of the proposition. If a proposition is true, then its truth value is denoted by T and if […]<\/p>\n","protected":false},"author":19,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"inline_featured_image":false,"footnotes":""},"categories":[2],"tags":[189,370,385,512,653,1433,1863],"class_list":["post-4317","post","type-post","status-publish","format-standard","hentry","category-algebra","tag-biconditional-stateme","tag-conditional-statement","tag-conjunction","tag-disjunction","tag-false","tag-proposition","tag-true"],"acf":[],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/posts\/4317","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/users\/19"}],"replies":[{"embeddable":true,"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/comments?post=4317"}],"version-history":[{"count":0,"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/posts\/4317\/revisions"}],"wp:attachment":[{"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/media?parent=4317"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/categories?post=4317"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/tags?post=4317"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}